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Abstract: The main purpose of this paper is to investigate the uniqueness of transcendental meromorphic functions that share four values in one angular domain which is an unbounded subset of the whole complex plane. From one of our main results, a question of J.H. Zheng [J.H. Zheng, On uniqueness of meromorphic functions with shared values in one angular domain, Complex Var. Elliptic Equ. 48 (9) (2003) 777–785] is completely answered. Furthermore, we give an example to explain the necessity of the condition in our results. [Copyright &y& Elsevier]

Abstract: In this paper, we will prove some uniqueness theorems of meromorphic functions whose derivatives share four distinct small functions. The results in this paper improve those given by R. Nevanlinna, L. Yang, G.D. Qiu, and other authors. An example is provided to show that the results in this paper are best possible. [Copyright &y& Elsevier]

Abstract: Using the idea of weighted sharing, we prove some results on uniqueness of meromorphic functions with three weighted sharing values. The results in this paper improve those given by H.X. Yi, T.C. Alzahary and H.X. Yi, T.C. Alzahary, I. Lahiri and N. Mandal, and other authors. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with a uniqueness theorem of two meromorphic functions that have three weighted sharing values and one pair of values. The results in this paper improve those given by G.G. Gundersen, G. Brosch, T.C. Alzahary, T.C. Alzahary and H.X. Yi, I. Lahiri and P. Sahoo, and other authors. [Copyright &y& Elsevier]

Abstract: In this paper, we deal with a uniqueness theorem of two meromorphic functions that have three weighted sharing values and a sharing set with two elements. The results in this paper improve those given by G. Brosch, K. Tohge, T.C. Alzahary and H.X. Yi and other authors. [Copyright &y& Elsevier]

Abstract: A uniqueness theorem for two distinct non-constant meromorphic functions that share three values of finite weights is proved, which generalizes two previous results by H.X. Yi, and X.M. Li and H.X. Yi. As applications of it, many known results by H.X. Yi and P. Li, etc. could be improved. Furthermore, with the concept of finite-weight sharing, extensions on Osgood–Yang''s conjecture and Mues'' conjecture, and a generalization of some prevenient results by M. Ozawa and H. Ueda, ect. could be obtained. [Copyright &y& Elsevier]

Abstract: In this paper, we study the growth of solutions of a first-order linear differential equation and that of a second-order linear differential equation. From this we obtain some uniqueness theorems of a nonconstant entire function and its first derivative having the same fixed points with the same multiplicities. The results in this paper also improve some known results. Some examples show that the results in this paper are best possible. [Copyright &y& Elsevier]

Abstract: In this paper, we give the definition of iterated order to classify functions of fast growth in the unit disc, and investigate the growth of solutions of linear differential equations with analytic coefficients of iterated order in the unit disc. We obtain several results concerning the iterated order of solutions. [Copyright &y& Elsevier]

Using the idea of weighted sharing, we prove some results on uniqueness of meromorphic functions sharing three values which improve some results given by H.-X. Yi, I. Lahiri, X. Hua and other authors. [Copyright &y& Elsevier]

Let f be a nonconstant entire function, and let k (⩾2) be an integer. We denote by Ef(z)={z∈C: f(z)=z, counting multiplicities} the set consisting of all the fixed points of f. This paper proves that if f and f′ have the same fixed points, namely, Ef(z)=Ef′(z), and if f(k)(z)=z whenever f(z)=z, then f≡f′. [Copyright &y& Elsevier]

Using the idea of weighted sharing of values, we study the problem of uniqueness of meromorphic functions that share three values. The results in this paper improve all theorems given by Lahiri in Nagoya Math. J. 161 (2001) 193–206. Examples are provided to show that some results in this paper are sharp. [Copyright &y& Elsevier]

This paper studies the uniqueness problem on entire function that share a finite, nonzero value CM with their derivatives and proves two main theorems which generalize some results given by Jank, Mues and Volkmann, P. Li and C.C. Yang, H.L. Zhong etc. An example shows that the condition of one of our theorems is necessary. [Copyright &y& Elsevier]

Abstract: This paper studies the uniqueness problem on entire function that share a finite, nonzero value with their linear differential polynomials and proves some theorems which generalize some results given by Jank, Mues and Volkmann, P. Li, J.P. Wang and H.X. Yi. [Copyright &y& Elsevier]